Australia’s carbon price has been repealed, leaving the nation with no legislated policy to achieve even the minimum 5% greenhouse emissions reduction target it has inscribed in international agreements.

The government said it would now achieve the 5% target through its as-yet-unlegislated Direct Action competitive grants policy, which the environment minister, Greg Hunt, insisted was a “policy for the long term”.

While the prime minister hailed the demise of the “useless, destructive [carbon] tax” and promised that the Coalition would “never do anything that damages the economy”, he repeatedly refused to rule out ever introducing a carbon price in the future.

The opposition leader, Bill Shorten, said Labor’s climate policy for the next election would include an emissions trading scheme and accused Abbott of “sleepwalking Australia towards an environmental and economic disaster”.

Setting up renewed bitter debate over climate policy, Shorten said the Labor party would not support Direct Action, which was a “boondoggle” constructed for “internet trolls … and right-wing shock jocks”.

Abbott said if the public ever elected Shorten they would know that “the carbon tax comes back”. The leader of government business in the house, Christopher Pyne, vowed that the Coalition would “hang this around [Shorten’s] neck until election day … he has given the Coalition a whole new lease of life.”

Complicating the picture is the Palmer United party (PUP), which has said it would vote for legislation setting up Direct Action only if the government accepted its plan for a “dormant” emissions trading scheme.

The government has already appropriated the funding for Direct Action and has previously said it would enact some parts of its policy without legislation. Hunt refused to “contemplate” that scenario on Thursday, saying he was intent on getting the scheme through the upper house.

After eight years of bitter political debate, during which climate policy dominated three election campaigns and contributed to the demise of two prime ministers, then last week’s Senate drama in which the repeal was again defeated and this week’s lengthy last-gasp debate, the Senate voted on Thursday morning to make good Abbott’s “pledge in blood” to “axe the tax”.

The government was backed by seven of the new crossbench senators, including the three PUP senators, Liberal Democrat senator David Leyonhjelm, Family First senator Bob Day, Motoring Enthusiast senator Ricky Muir and the DLP senator John Madigan. The independent senator Nick Xenophon was unwell and absent from the chamber.

Only Labor and the Greens voted against repealing the carbon pricing scheme they introduced, which came into effect two years ago.